利用差动旋转恒星中的低T/W动力学不稳定性确定状态方程的刚度
Determining the stiffness of the equation of state using low T/W dynamical instabilities in differentially rotating stars
摘要：
我们调查的性质低T/W动力学不稳定性在不同范围内的刚度的状态方程在差分旋转的恒星。这里T是转动动能，而W是引力结合能。我们分析这些不稳定性的线性扰动分析和三维流体动力学模拟。通过求解沿恒星赤道面的本征值问题，探测到了差动自转恒星的不稳定简正模。低T/W动力学不稳定性的物理机制也定性地证实了由共转障碍引起的共转和表面之间的声波的散射。因此，我们可以画出现有的脉动模式不稳定，由于放大反射的声波从共转障碍。线性分析中不稳定模态的本征频率和本征函数的特征与牛顿引力下三维流体动力学模拟的特征基本一致。此外，本征函数的性质，振荡之间的共转和表面的不稳定的恒星需要重新解释的脉动模式在差分旋转的恒星。最后，我们提出了一种方式，通过直接检测模式分解的引力波形来约束状态方程的刚度。
英文摘要：
We investigate the nature of low T/W dynamical instabilities in various ranges of the stiffness of the equation of state in differentially rotating stars. Here T is the rotational kinetic energy, while W the gravitational binding energy. We analyze these instabilities in both a linear perturbation analysis and a three-dimensional hydrodynamical simulation. An unstable normal mode of a differentially rotating star is detected by solving an eigenvalue problem along the equatorial plane of the star. The physical mechanism of low T/W dynamical instabilities is also qualitatively confirmed by a scattering of sound waves between corotation and the surface caused by the corotation barrier. Therefore, we can draw a picture of existing pulsation modes unstabilized due to an amplified reflection of sound waves from the corotation barrier. The feature in the eigenfrequency and eigenfunction of the unstable mode in the linear analysis roughly agrees with that in the three-dimensional hydrodynamical simulation in Newtonian gravity. Moreover, the nature of the eigenfunction that oscillates between corotation and the surface for an unstable star requires reinterpretation of pulsation modes in differentially rotating stars. Finally, we propose a manner by which to constrain the stiffness of the equation of state by the direct detection of mode decomposed gravitational waveforms.
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